Facts of the case

After they were sentenced to death in Arizona, Walter LaGrand and Karl LaGrand filed petitions for writs of habeas corpus. Among other things, Walter's petition claimed that execution by lethal gas constituted cruel and unusual punishment under the Eighth Amendment. Ultimately, the Court of Appeals found the claim unripe until and unless Walter chose gas as his method of execution and denied his petition. Under Arizona law, lethal injection is the default form of execution. Separately, as part of its ultimate order, the Court of Appeals stayed Karl's execution and enjoined Arizona from executing anyone by means of lethal gas. Subsequently, the Court of Appeals ultimately denied Walter a stay of execution but restrained and enjoined the Arizona from executing him by means of lethal gas.

Question

Did Walter LaGrand waive his claim that execution by lethal gas constitutes cruel and unusual punishment under the Eighth Amendment by electing to be executed by lethal gas, when Arizona's default form of execution is lethal injection?